solving large instances of the quadratic cost partition problem on dense graphs by data-cor精选.pdf
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Solving Large Instances of the Quadratic Cost
Partition Problem on Dense Graphs by
Data-Correcting Algorithms: a Computational
Study
Boris Goldengorin, Marius de Vink
20th August, 1999
Abstract
The Data-Correcting Algorithm (DCA) corrects the data of a hard problem
instance in such a way that we obtain an instance of a well solvable special
case. For a given prescribed accuracy of the solution, the DCA uses a branch
and bound scheme to make sure that the solution of the corrected instance
satisfies this given prescribed accuracy. We describe the “hardness” of ran-
domly generated instances of the Quadratic Cost Partition Problem (QCP)
by the density of the corresponding graphs as well as by the cardinality of an
optimal solution of the QCP. We study the behaviour of the DCAs through
the number of search levels of the so called Preliminary Preservation Al-
gorithm and average computational times. We report average computational
times of the DCA for instances of dense graphs with the number of vertices
up to 500 which can be solved on a standard PC within 10 minutes.
Keywords: global maximum, submodular functions, quadratic program-
ming
Department of Econometrics and Operations Research, University of Groningen, P.O.Box 800,
9700 AV Groningen, The Netherlands. Corresponding author. Tel. +31-50-363 3794 fax: +31-50-363
3720. e-mail: B.Goldengorin@eco.rug.nl
1
1. Scope and purpose
Given a graph with nonnegative weights on the edges and real numbers as weights of
vertices. For every set of vertices, the difference between the sum of vertex weights
of
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